As K-12 mathematics standards shift toward emphasizing both conceptual and procedural knowledge in secondary courses such as algebra and geometry, the struggles for students with disabilities become more pronounced. To address these challenges, research has commonly explored the use of technology to aid in the teaching of students with…

The effect of metacognitive scaffolding for learning by teaching was investigated and compared against learning by being tutored. Three versions of an online learning environment for learning algebra equations were created: (1) APLUS that allows students to interactively teach a synthetic peer with a goal to have the synthetic peer pass the quiz…

We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the…

Background: Many engineering students fail to proceed through required prerequisite mathematics courses. Since these courses strongly influence engineering student attrition, we should examine to what degree these courses truly serve as prerequisites for following engineering coursework. Purpose/Hypothesis: We examined two research questions:…

This study was conducted to assess the students' level of abilities in solving algebraic word problems which is a main component in Science, Technology, Engineering and Mathematics (STEM). It also aims to determine the students' difficulties in solving these problems by using Newman's Model of Error Analysis (NMEA). Furthermore, this study was…

This study aims to describe how subjects construct explicit warrant derived from implicit warrant when completing mathematical proof. This research was conducted on seventeen students of mathematics education study programs by providing tests on vector material in elementary linear algebra courses. The test results show that there are four…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…

This study aims to describe the ability of students' mathematical connections in solving problems in the circle equation material through transposition studies. The method in this research is a descriptive qualitative approach, the techniques used in the study are tests, interviews, and documentation to explore data in research. Test and interview…

Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how…

With limited time available in the classroom, e-learning tools can supplement in-class learning by providing opportunities for students to study and learn outside of class. Such tools can be especially helpful for students who lack adequate prior preparation. However, one critical issue is ensuring that students, especially those in need of…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

We review the history and previous literature on radical equations and present the rigorous solution theory for radical equations of depth 2, continuing a previous study of radical equations of depth 1. Radical equations of depth 2 are equations where the unknown variable appears under at least one square root and where two steps are needed to…

In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of…

Mathematical models that are constructed through modeling activities should be appropriate for the situation at hand. In this study, we seek to monitor the modeling routes of different learners as well as their modeling sub-competencies in order to learn how these are related to the semiotic characteristics of the resulting mathematical models.…

The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed…